Yet understanding the state of the tape and what it represents gets increasingly difficult the more abstract you get. Running a non-trivial programme in a Turing machine is as hard to inspect as disassembling one in a standard computer. The complexity does not lie on the general computing platform, but in the interpretation that we derive from its state - and, as long as the platform is turing complete, by definition, we will end up running inescrutable programs (because we can!).

Ah, so you've encountered jQuery.

While probably possible, writing a Turing machine in code/software [incl. unit tests] is a trivial Saturday afternoon task. The amount of effort/cost is just orders of magnitude different.